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A348580
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Expansion of e.g.f. exp(x) / (1 - sin(x)).
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3
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1, 2, 5, 15, 53, 217, 1015, 5355, 31513, 204857, 1458875, 11299695, 94600373, 851419597, 8198959735, 84124450035, 916270051633, 10559066809937, 128362804540595, 1641730799916375, 22037407161945293, 309782122281453877, 4551072446448773455, 69747642031977698715
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(n,k) * A000111(k+1).
a(n) ~ 2^(n + 7/2) * n^(n + 3/2) / (Pi^(n + 3/2) * exp(n - Pi/2)). - Vaclav Kotesovec, Oct 25 2021
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MAPLE
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b:= proc(u, o) option remember; `if`(u+o=0, 1,
add(b(o-1+j, u-j), j=1..u))
end:
a:= n-> add(binomial(n, k)*b(k+1, 0), k=0..n):
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MATHEMATICA
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nmax = 23; CoefficientList[Series[Exp[x]/(1 - Sin[x]), {x, 0, nmax}], x] Range[0, nmax]!
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PROG
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(PARI) my(x='x+O('x^40)); Vec(serlaplace(exp(x)/(1-sin(x)))) \\ Michel Marcus, Oct 24 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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